Introduction to Surface Tension

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Introduction:

Intermolecular Forces:

  • Between any two molecules, there exists a force of attraction. This force is called the intermolecular force.
  • These intermolecular forces of attraction are of two types. a) cohesive force and b) adhesive force.

Cohesive Force and Cohesion:

  • The attractive force between the two molecules of the same substance is called as a cohesive force and the attraction itself is called cohesion.
  • e.g. attraction between water and water molecules.

Adhesive Force and Adhesion:

  • The attractive force between the two molecules of the different substance is called an adhesive force and the attraction itself is called adhesion.
  • e.g. attraction between water and glass molecules.


Phenomenon: Water wets glass:

  • The attractive force between the two molecules of the same substance is called as a cohesive force and the attractive force between the two molecules of the different substance is called an adhesive force.
  • In case of water, the cohesive force between water molecules is very less compared to the adhesive force between glass and water molecules. Thus there is a strong attraction between water and glass molecules. Hence water wets glass.

Phenomenon: Mercury does not wet glass:

  • The attractive force between the two molecules of the same substance is called as a cohesive force and the attractive force between the two molecules of the different substance is called an adhesive force.
  • In case of mercury, the cohesive force between its molecules is very strong compared to negligible adhesive force between glass and mercury molecules. Thus there is a strong attraction between mercury molecules and almost no attractive force between glass and mercury molecules. Hence mercury does not wet glass.

Range of molecular attraction (r) :

  • The maximum distance between two molecules up to which the intermolecular forces are effective is called the range of molecular attraction.
  • It is of order 10-9 m.

Sphere of Molecular Influence :

  • A sphere drawn by taking the radius equal to the range of molecular attraction and centre as the centre of the molecule is called sphere of molecular influence.

Surface Tension Sphere of Influence

Concept of Surface Tension:

  • Surface tension or force of surface tension is the force per unit length of an imaginary line drawn in any direction on the free surface of a liquid, the line of action of the force being on the surface and at right angles to the length of the imaginary line.

Dimensions of Surface tension:

Surface Tension (T)  = Force (F) / Effective Length (L)

∴   [T] = [F] / [L]

∴   [T] = [L1M1T-2] / [L1]

∴   [T] = [L0M1T-2]

Thus the dimensions of surface tension are [L0M1T-2].

S.I. Unit of Surface Tension:

Surface Tension (T)  = Force (F) / Effective Length (L)

∴   S.I. unit of T = S.I. unit of F /S.I. unit of L

∴    S.I. unit of surface tension= newton (N) / metre (m)

Thus S.I. unit of surface tension is N/m and c.g.s. unit is dyne/cm.

Explanation of Surface Tension on the Basis of Molecular Theory:

 

Surface Tension Molecular Theory

  • Consider three molecules A, B and C in a liquid, such that molecule A is well inside the liquid, molecule B is close to the free surface and the molecule C is on the free surface.
  • The sphere of influence of the molecule A is completely inside the liquid, and hence it will be acted upon by equal forces in all directions and these forces will balance one another and the net force acting on it is zero.
  • For the molecule B, a part of upper half of the sphere of influence is in the air, which contains air molecules.  Air molecules exert very negligible adhesive forces on molecule B.  Therefore, the cohesive forces due to molecules in the liquid remains unbalanced and thus a net force in downward direction acts on the molecule.
  • For the molecule C, the upper half of the sphere of influence is completely in the air. Due to this, the force of attraction due to the molecules inside the lower half of the sphere will remain unbalanced.  This molecule experiences the maximum possible unbalanced force in the downward direction.
  • Thus the molecules on the surface and in a surface film of thickness equal to the range of molecular attraction of the liquid molecule experience a net force in the downward direction.  The magnitude of force depends upon the distance of the molecule from the free surface.  The behaviour of this film is different from that of the rest of the liquid.  It is called the surface film.  This film behaves like a film which is under tension.  This phenomenon is known as surface tension.
  • If any molecule is brought to the surface from the liquid, the work is to be done against this net downward force. This work increases the potential energy of the surface. But the liquid surface will have the tendency to have minimum potential energy. So a minimum number of molecules remains on the surface of the liquid.
  • Thus the free surface of a liquid behaves like a stretched elastic membrane and has a tendency to contract so as to minimise its surface area.


Concept of Surface Energy:

  • A molecule on the surface of a liquid experiences a downward pull due to surface tension.  If a molecule deep inside the liquid is to be lifted up towards the fine surface, as soon as it enters the surface film, work will have to be done to lift it further against the unbalanced downward forces of molecular attraction.
  • This work will be stored in the molecule as potential energy. This is true of every molecule on the surface film and surface film possesses a certain amount of potential energy. Thus the molecules in surface film possess extra energy. This energy is called as surface energy.
  • Its S.I. unit is J and its dimensions are [L2M1T-2].

Relation Between Surface Tension and Surface Energy:

Surface Tension Surface Energy

  • Consider a rectangular frame ABCD in which side CD is made of loose write and other three sides are fixed. The frame is immersed in a soap solution and taken out and held horizontally. A film of soap solution will be formed on the frame and it will at once try to shrink and pull the loose wire CD towards AB. If the length of loose wire CD is  ‘l’ and the film is of finite thickness, therefore the film will be in contact with the wire both on the upper surface as well as along its lower surface.  Hence the length of the wire in contact with the film is ‘ 2l ‘.  The force acting on the wire is directed towards AB, per unit length of the contact line is surface tension (T). By definition of surface tension, we have

T = F / 2l

∴    F  =  T . 2 l     …  (1)

  • Imagine an external force is applied on CD which is equal and opposite to force F Let the wire at CD moves to C’D’ through small distance dx.  Then the work done against the force of surface tension is given by

dW  =  F.dx         …  (2)

From equations (1) and (2),

dW = T.2l. dx

But,  2l . dx = dA = increase in Area of both the surface of the film.

∴  dW   =  T.dA

This work done is stored inside the films as potential energy dU.

∴   dU  =  T.dA

 

  • If, initially CD is very close to AB, initial energy and initial area of the film can be taken as zero and dU and dA can be treated as total energy and the total area of the film respectively.

∴  T  =  dU / dA

  • This expression indicates that surface tension is equal to surface energy per unit area of the surface film.
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